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Can you draw a continuous line through $16$ numbers on this grid so that the total of the numbers you pass through is as high as possible?

You may start and finish where you like, and go horizontally, vertically or diagonally but you may only pass through a number once and the line must not cross itself at any point.

If you repeat this but only go horizontally and vertically and never go diagonally, what is the highest score then?